2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64787For completely multiplicative functions f(n) taking values 1 and -1, under certain conditions on f(n) we show that f(n) changes sign at least x exp(-7(log log x)sqrt(log x)) times as n runs through the integers <= x.12 pages, accepted by Journal of Number TheoryNumber Theory11N56text